Final answer:
The critical z-value for a left-tailed test with α = 0.01 is approximately -2.326, indicating that any z-score less than this value would lead to rejection of the null hypothesis.
Step-by-step explanation:
To find the critical z-value for a left-tailed test with an alpha (α) of 0.01, you need to find the z-score that leaves 0.01 of the probability in the left tail of the standard normal distribution. This is known as α. To find this, you can use a standard normal probability table or a calculator's inverse normal function.
According to these tools, the critical z-value that corresponds to α = 0.01 is approximately -2.326. This means that if the z-score calculated from the sample data is less than -2.326, we would reject the null hypothesis in a left-tailed test.